Nuprl Lemma : es-interface-predecessors-iseg
∀[Info:Type]. ∀es:EO+(Info). ∀X:EClass(Top). ∀e,e':E(X). (≤(X)(e') ≤ ≤(X)(e) ⇐⇒ e' ≤loc e )
Proof
Definitions occuring in Statement :
es-interface-predecessors: ≤(X)(e),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
iseg: l1 ≤ l2,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
less_than': less_than'(a;b),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
nat: ℕ,
es-E-interface: E(X),
ge: i ≥ j ,
less_than: a < b,
squash: ↓T,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
es-le: e ≤loc e' ,
label: ...$L... t,
sq_type: SQType(T),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
cand: A c∧ B,
bfalse: ff,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
cons: [a / b],
last: last(L),
subtract: n - m,
select: L[n],
es-E: E
Latex:
\mforall{}[Info:Type]. \mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}e,e':E(X). (\mleq{}(X)(e') \mleq{} \mleq{}(X)(e) \mLeftarrow{}{}\mRightarrow{} e' \mleq{}loc e )
Date html generated:
2016_05_17-AM-06_57_03
Last ObjectModification:
2016_01_17-PM-06_40_17
Theory : event-ordering
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